Geometric Construction: Finding the Correct Median in a Triangle

To solve this problem, we must identify which line segment in triangle ABC is the median.

First, review the definition: a median in a triangle connects a vertex to the midpoint of the opposite side. Now, in triangle ABC:

• Point A represents the vertex.
• Point E lies on line segment AB.
• Line segment EC needs to be checked to see if it connects vertex E to point C.

From the diagram, it appears that E is indeed the midpoint of side AB. Thus, line segment EC connects vertex C to this midpoint.

This fits the definition of a median, verifying that EC is the median line segment in triangle ABC.

Therefore, the solution to the problem is: $\text{EC}$.